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Does either of the player have a dominant strategy
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- Suppose we have two ice cream sellers, Blue Cool Ice Cream and Red Mango Ice Cream, deciding where to locate along a 1 kilometer long linear beach. Beachgoers are uniformly spread out everywhere along the beach. They do not like walking, and they view the ice cream from the two sellers as homogenous goods. Because of this, they will always buy from the nearest seller. The sellers cannot choose their price, only the location. A strategy for a player in this game is a distance between 0m and 1000m, which represents where the player will locate. For example, a distance of 0m is a strategy. The payoffs are the percentages of the market that each seller captures (depending on their two strategies). For example, if Blue Cool chooses 0m and Red Mango chooses 1000m, their payoffs are 50% and 50%. If the two sellers locate at exactly the same spot, they share the market and get 50% each. Suppose each player can only choose from 5 locations: 0m, 250m, 500m, 750m, 1000m. Is playing 0m is a…Two firms, Snow Kings and Ski Express, at Denver International Airport have franchises to carry passengers to and from the mountains. These two firms compete through advertising. Their payoff matrix is below. Profits per customer are represented in the following format (Snow Kings, Ski Express Snow Kings Advertise Don't Advertise Advertise 25, 15 15, 20 Ski Express Don't Advertise 30,0 40,5 What combination of strategies achieves the Nash equilibrium in this game? a) 25,25 (Advertise, Advertise) b) 15,20 (Advertise, Advertise) c) 25,0 (Advertise, Don't Advertise) d) 40,5 (Advertise, Don't Advertise)O Cell A O Cell C O Cell E O Cell I None of the above
- Two oligopolistic aluminium manufacturers are engaged in bitter competition with one another, Both firms, Big Aluminium Giant (BAG) and Little Aluminium Giant (LAG), are deciding whether to expand capacity or not. The table below shows payoffs for the firms under various scenarios. The first number in each cell is the payoff of LAG. Suppose the game is played once and each firm has to make its decision simultaneously. Does BAG have a dominant strategy? Explain clearly. Does LAG have a dominant strategy? Explain clearly. Big Aluminium Giant (BAG) Don't Expand 3, 4 4, 2 Еxpand Little Aluminium Giant Don't Expand 2, 3 Expand 1, 1 For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac).Two oligopolistic firms have to decide on the pricing strategy. Each can either choose either a high or a low price. If they both choose a high price, each will make $12 million, but if they both choose a low price, each will make $ 8 million. If one sets a high price and other a low one, the low-priced firm will make $16 million, but the high-priced firm will make only $4 million. It is illegal for each firm to communicate with each other. a) Which strategy would both of them ultimately opt for? b) What would be the pay-off for this strategy?Player 1 can stay at home or fly to New York, in which case Player 2 can meet Player 1, who can then buy a drink for Player 2. See the game below. Which of the following completely describes a possible strategy for Player 1? 1 Fly to New York Stay home Stay home Stay home and Don't buy drink Fly to New York and Meet Stay home or Fly to New York 2 Meet Don't meet 0,0 1 Buy drink Don't buy drink -2,0 1,2 -1, -1
- Once again, two ice cream truck vendors, A and B, are playing a simultaneous pricing game. If only one of the vendors prices low, he gets all the customers for a payoff of 12, while the other vendor gets no customers and a payoff of zero. If both vendors price high, they each get a payoff of 6. If both price low, they each get a payoff of 5. Suppose that the above game is repeated indefinitely, and together the vendors adopt a trigger strategy such that they would start charging the low price only if the other vendor charged a low price last time. Provided that the vendors stick to their new strategy, what would be the Nash equilibrium going forward? a) Both the vendors price high b) Both the vendors price low c) Vendor A prices high, vendor B prices low d) Vendor B prices high, vendor A prices lowRefer to the normal-form game of price competition in the payoff matrix below Firm B Low Price High Price Firm A Low Price 0, 0 50, −10 High Price −10, 50 20, 20 Suppose the game is infinitely repeated, and the interest rate is 20 percent. Both firms agree to charge a high price, provided no player has charged a low price in the past. This collusive outcome will be implemented with a trigger strategy that states that if any firm cheats, then the agreement is no longer valid, and each firm may make independent decisions. Will the trigger strategy be effective in implementing the collusive agreement? Please explain and show all necessary calculations.In the collusion game, collusion was only sustainable in the infinite horizon repeated game. One Nash Equilibrium of that game can be found when all players play a “grim trigger” strategy, where they collude until an opponent chooses to compete, and then compete for all future rounds as a punishment. In such a game, if the one period bonus that comes from competing is low enough, firms always collude and the punishment is never triggered. Is the punishment (vowing to compete forever after one deviates) realistic, especially if firms can communicate freely? Why or why not? (Hint: Is a grim trigger Nash Equilibrium a Subgame Perfect Nash Equilibrium? What kinds of Nash Equilibria does Subgame erfection rule out in sequential games?)
- Here is a table representing the gains for the server if he serves on his opponent's forehand or backhand and for the receiver the gains if he returns on his forehand or backhand. Each player can choose to play the forehand or the backhand of the other player : Server D R D 50,50 80, 20 R 90,10 |20, 80 Receiver D Determine the Nash equilibrium(s) (pure strategies and mixed strategies).Consider the 2-player, zero-sum game "Rock, Paper, Scissors". Each player chooses one of 3 strategies: rock, paper, or scissors. Then, both players reveal their choices. The outcome is determined as follows. If both players choose the same strategy, neither player wins or loses anything. Otherwise: • "paper covers rock": if one player chooses paper and the other chooses rock, the player who chose paper wins and is paid 1 by the other player. "scissors cut paper": if one player chooses scissors and the other chooses paper, the player who chose scissors wins and is paid 1 by the other player. "rock breaks scissors": if one player chooses rock and the other player chooses scissors, the player who chose rock wins and is paid 1 by the other player. We can write the payoff matrix for this game as follows: rock paper scissors rock 0 -1 1 paper 1 0 scissors -1 1 -1 0 2. Suppose now we alter the game so that whenever Colin chooses "paper" the loser pays the winner 3 instead of 1: rock paper…Speedy Bike's Advertising Power Bike's Advertising Budget Large Budget Small Large Small A $20 B $18 $20 с $35 $18 $35 D $25 $25 Refer to the payoff matrix. Suppose that Speedy Bike and Power Bike are the only two bicycle manufacturing firms serving the market. Both can choose large or small advertising budgets. If this is a one-time, simultaneous game, which cell represents the final outcome we would expect to occur?